It likely won’t amount to even a hiccup in Syria’s bloodletting, but yesterday’s resignation of Kofi Annan must serve as a warning to us. The spectacular failure of his mission shows the limits of America’s policy of relying too much on international cooperation.

Even Annan, revered by one-worlders as their “secular pope,” yesterday blamed the United Nations Security Council (the international community’s “Vatican”?) for much of this failure.

“When the Syrian people desperately need action — there continues to be finger-pointing and name-calling in the Security Council,” he told reporters in Geneva.

True enough. Russia and China vetoed three council resolutions proposed by the three other main powers. Normally civilized diplo-speak then turned ugly.

“We hear that the Obama administration wants to establish a dialogue with the international community [through] the Security Council,” Russian UN ambassador Vitaly Churkin snarked early on in the crisis. First, he advised, we must leave behind sensibilities learned at Stanford University — the alma mater of our UN ambassador, Susan Rice.

But why the Sam Hill would America want to subject itself to such ridicule to begin with? And then repeat it three times?

When the council finally united behind something — Annan’s mission — Rice endlessly hinted that we wouldn’t support it blindly. Yet it wasn’t until after yet another humiliating Russian veto a couple of weeks ago that she finally said we’d look for Syria solutions “outside this council.”

That was 17 months into the crisis that’s left 17,000 dead and counting, and which still threatens to revive al Qaeda, ignite the whole region in chemical fumes and (if Bashar al-Assad wins) embolden our enemy Iran while weakening our Israeli, Arab and Turkish allies.

As soon as he accepted the job of UN and Arab League Syria envoy in March, Annan devised a new “peace” plan: First create a “dialogue” between Syria’s butchering tyrant and those who’ve already sacrificed so much to topple him.

Not only unrealistic, the idea also junked the Arab League’s call to first remove Assad from power — and he was supposedly the league’s envoy, too.

It was downhill from there. Annan endlessly traveled between Moscow, Beijing and Tehran, while spending little time on the ground in Damascus. With no single success, his staff nevertheless kept expanding, hiring international “observers.”

With no America to lead, the Annan plan remained the only game in town — until Annan finally sensed that even his biggest fans were losing faith. With his memoir “Interventions: A Life in War and Peace” about to hit the stands, he yesterday quit his self-described “mission impossible.”